Problem: ${\sqrt[3]{10000} = \text{?}}$
Answer: $\sqrt[3]{10000}$ is the number that, when multiplied by itself three times, equals $10000$ First break down $10000$ into its prime factorization and look for factors that appear three times. So the prime factorization of $10000$ is $2\times 2\times 2\times 2\times 5\times 5\times 5\times 5$ Notice that we can rearrange the factors like so: $10000 = 2 \times 2 \times 2 \times 2 \times 5 \times 5 \times 5 \times 5 = (2\times 2\times 2) \times (5\times 5\times 5) \times 2\times 5$ So $\sqrt[3]{10000} = \sqrt[3]{2\times 2\times 2} \times \sqrt[3]{5\times 5\times 5} \times \sqrt[3]{2\times 5}$ $\sqrt[3]{10000} = 2\times 5 \times \sqrt[3]{2\times 5}$ $\sqrt[3]{10000} = 10 \sqrt[3]{10}$